ABJM到BMN的双重标度极限：指标与鼓泡几何
ABJM to BMN in a Double Scale Limit: Indices and Bubbling Geometries
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中文总结 AI 辅助
该论文在双重标度极限下建立了ABJM理论与秩q BMN矩阵模型的对应关系，通过引力几何和超对称指标分解证明了其等价性。
中文摘要 AI 辅助
我们研究了$U(N)_k\times U(N)_{-k}$ ABJM理论的双重标度极限，其中$N,k\to\infty$且$N/k^2\to\nu\in(0,\infty)$，固定正磁单极电荷$q$。在该极限下，彭罗斯几何保留了一个有限半径的紧致零圆，磁单极电荷为$q$的扇区携带$q$单位的纵向动量。因此，它自然地与秩为$q$的BMN矩阵模型相关联，而$\nu$确定了其无量纲耦合常数。我们从引力和超对称指标两方面建立了这一关系。在引力侧，我们对Donos–Simón半BPS几何的Hopf商取双重标度极限。承载增长背景通量的圆盘变为无限导电平面，而剩余的有限圆盘再现了Lin–Maldacena静电问题。它们的量子化通量直接映射到标记BMN真空的配分数据。在场论侧，从有限$N$、有限$k$的ABJM局域化公式出发，我们证明了在固定正磁单极电荷$q$时，ABJM超共形指标在横向 fugacity 上逐系数分解为一个普适中性贡献和秩为$q$的BMN矩阵模型的精细Witten指标，以及纵向动量权重。中性贡献恰好是零磁单极电荷极限指标。因此，除以这个普适因子就分离出对所有超对称真空求和的BMN指标。
英文摘要
We study a double scale limit of $U(N)_k\times U(N)_{-k}$ ABJM theory, with $N,k\to\infty$ and $N/k^2\toν\in(0,\infty)$, at fixed positive total monopole charge $q$. In this limit, the Penrose geometry retains a compact null circle of finite radius, and the sector of monopole charge $q$ carries $q$ units of longitudinal momentum. It is therefore naturally associated with the rank-$q$ BMN matrix model, while $ν$ fixes its dimensionless coupling. We establish this relation from both gravity and the supersymmetric index. On the gravity side, we take the double scale limit of Hopf quotients of the Donos--Simón half-BPS geometries. The disk carrying the growing background flux becomes an infinite conducting plane, while the remaining finite disks reproduce the Lin--Maldacena electrostatic problem. Their quantized fluxes map directly to the partition data labeling BMN vacua. On the field-theory side, starting from the finite-$N$, finite-$k$ ABJM localization formula, we prove that, at fixed positive monopole charge $q$, the ABJM superconformal index factorizes coefficientwise in the transverse fugacities into a universal neutral contribution and the refined Witten index of the rank-$q$ BMN matrix model, together with the longitudinal momentum weight. The neutral contribution is precisely the limiting zero-monopole-charge index. Dividing by this universal factor therefore isolates the BMN index summed over all its supersymmetric vacua.
发表机构
- School of Physics, Peking University（北京大学物理学院）
- Center for High Energy Physics, Peking University（北京大学高能物理中心）
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